- Main Page
- Modules
- Data Structures
- Files

# matrix.h

    00001 /*************************************************************************
    00002  *                                                                       *
    00003  * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
    00004  * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
    00005  *                                                                       *
    00006  * This library is free software; you can redistribute it and/or         *
    00007  * modify it under the terms of EITHER:                                  *
    00008  *   (1) The GNU Lesser General Public License as published by the Free  *
    00009  *       Software Foundation; either version 2.1 of the License, or (at  *
    00010  *       your option) any later version. The text of the GNU Lesser      *
    00011  *       General Public License is included with this library in the     *
    00012  *       file LICENSE.TXT.                                               *
    00013  *   (2) The BSD-style license that is included with this library in     *
    00014  *       the file LICENSE-BSD.TXT.                                       *
    00015  *                                                                       *
    00016  * This library is distributed in the hope that it will be useful,       *
    00017  * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
    00018  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
    00019  * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
    00020  *                                                                       *
    00021  *************************************************************************/
    00022
    00023 /* optimized and unoptimized vector and matrix functions */
    00024
    00025 #ifndef _ODE_MATRIX_H_
    00026 #define _ODE_MATRIX_H_
    00027
    00028 #include <ode/common.h>
    00029
    00030
    00031 #ifdef __cplusplus
    00032 extern "C" {
    00033 #endif
    00034
    00035
    00036 /* set a vector/matrix of size n to all zeros, or to a specific value. */
    00037
    00038 ODE_API void dSetZero (dReal *a, int n);
    00039 ODE_API void dSetValue (dReal *a, int n, dReal value);
    00040
    00041
    00042 /* get the dot product of two n*1 vectors. if n <= 0 then
    00043  * zero will be returned (in which case a and b need not be valid).
    00044  */
    00045
    00046 ODE_API dReal dDot (const dReal *a, const dReal *b, int n);
    00047
    00048
    00049 /* get the dot products of (a0,b), (a1,b), etc and return them in outsum.
    00050  * all vectors are n*1. if n <= 0 then zeroes will be returned (in which case
    00051  * the input vectors need not be valid). this function is somewhat faster
    00052  * than calling dDot() for all of the combinations separately.
    00053  */
    00054
    00055 /* NOT INCLUDED in the library for now.
    00056 void dMultidot2 (const dReal *a0, const dReal *a1,
    00057        const dReal *b, dReal *outsum, int n);
    00058 */
    00059
    00060
    00061 /* matrix multiplication. all matrices are stored in standard row format.
    00062  * the digit refers to the argument that is transposed:
    00063  *   0:   A = B  * C   (sizes: A:p*r B:p*q C:q*r)
    00064  *   1:   A = B' * C   (sizes: A:p*r B:q*p C:q*r)
    00065  *   2:   A = B  * C'  (sizes: A:p*r B:p*q C:r*q)
    00066  * case 1,2 are equivalent to saying that the operation is A=B*C but
    00067  * B or C are stored in standard column format.
    00068  */
    00069
    00070 ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
    00071 ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
    00072 ODE_API void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
    00073
    00074
    00075 /* do an in-place cholesky decomposition on the lower triangle of the n*n
    00076  * symmetric matrix A (which is stored by rows). the resulting lower triangle
    00077  * will be such that L*L'=A. return 1 on success and 0 on failure (on failure
    00078  * the matrix is not positive definite).
    00079  */
    00080
    00081 ODE_API int dFactorCholesky (dReal *A, int n);
    00082
    00083
    00084 /* solve for x: L*L'*x = b, and put the result back into x.
    00085  * L is size n*n, b is size n*1. only the lower triangle of L is considered.
    00086  */
    00087
    00088 ODE_API void dSolveCholesky (const dReal *L, dReal *b, int n);
    00089
    00090
    00091 /* compute the inverse of the n*n positive definite matrix A and put it in
    00092  * Ainv. this is not especially fast. this returns 1 on success (A was
    00093  * positive definite) or 0 on failure (not PD).
    00094  */
    00095
    00096 ODE_API int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);
    00097
    00098
    00099 /* check whether an n*n matrix A is positive definite, return 1/0 (yes/no).
    00100  * positive definite means that x'*A*x > 0 for any x. this performs a
    00101  * cholesky decomposition of A. if the decomposition fails then the matrix
    00102  * is not positive definite. A is stored by rows. A is not altered.
    00103  */
    00104
    00105 ODE_API int dIsPositiveDefinite (const dReal *A, int n);
    00106
    00107
    00108 /* factorize a matrix A into L*D*L', where L is lower triangular with ones on
    00109  * the diagonal, and D is diagonal.
    00110  * A is an n*n matrix stored by rows, with a leading dimension of n rounded
    00111  * up to 4. L is written into the strict lower triangle of A (the ones are not
    00112  * written) and the reciprocal of the diagonal elements of D are written into
    00113  * d.
    00114  */
    00115 ODE_API void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
    00116
    00117
    00118 /* solve L*x=b, where L is n*n lower triangular with ones on the diagonal,
    00119  * and x,b are n*1. b is overwritten with x.
    00120  * the leading dimension of L is `nskip'.
    00121  */
    00122 ODE_API void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
    00123
    00124
    00125 /* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal,
    00126  * and x,b are n*1. b is overwritten with x.
    00127  * the leading dimension of L is `nskip'.
    00128  */
    00129 ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
    00130
    00131
    00132 /* in matlab syntax: a(1:n) = a(1:n) .* d(1:n) */
    00133
    00134 ODE_API void dVectorScale (dReal *a, const dReal *d, int n);
    00135
    00136
    00137 /* given `L', a n*n lower triangular matrix with ones on the diagonal,
    00138  * and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix
    00139  * D, solve L*D*L'*x=b where x,b are n*1. x overwrites b.
    00140  * the leading dimension of L is `nskip'.
    00141  */
    00142
    00143 ODE_API void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
    00144
    00145
    00146 /* given an L*D*L' factorization of an n*n matrix A, return the updated
    00147  * factorization L2*D2*L2' of A plus the following "top left" matrix:
    00148  *
    00149  *    [ b a' ]     <-- b is a[0]
    00150  *    [ a 0  ]     <-- a is a[1..n-1]
    00151  *
    00152  *   - L has size n*n, its leading dimension is nskip. L is lower triangular
    00153  *     with ones on the diagonal. only the lower triangle of L is referenced.
    00154  *   - d has size n. d contains the reciprocal diagonal elements of D.
    00155  *   - a has size n.
    00156  * the result is written into L, except that the left column of L and d[0]
    00157  * are not actually modified. see ldltaddTL.m for further comments.
    00158  */
    00159 ODE_API void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);
    00160
    00161
    00162 /* given an L*D*L' factorization of a permuted matrix A, produce a new
    00163  * factorization for row and column `r' removed.
    00164  *   - A has size n1*n1, its leading dimension in nskip. A is symmetric and
    00165  *     positive definite. only the lower triangle of A is referenced.
    00166  *     A itself may actually be an array of row pointers.
    00167  *   - L has size n2*n2, its leading dimension in nskip. L is lower triangular
    00168  *     with ones on the diagonal. only the lower triangle of L is referenced.
    00169  *   - d has size n2. d contains the reciprocal diagonal elements of D.
    00170  *   - p is a permutation vector. it contains n2 indexes into A. each index
    00171  *     must be in the range 0..n1-1.
    00172  *   - r is the row/column of L to remove.
    00173  * the new L will be written within the old L, i.e. will have the same leading
    00174  * dimension. the last row and column of L, and the last element of d, are
    00175  * undefined on exit.
    00176  *
    00177  * a fast O(n^2) algorithm is used. see ldltremove.m for further comments.
    00178  */
    00179 ODE_API void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
    00180         int n1, int n2, int r, int nskip);
    00181
    00182
    00183 /* given an n*n matrix A (with leading dimension nskip), remove the r'th row
    00184  * and column by moving elements. the new matrix will have the same leading
    00185  * dimension. the last row and column of A are untouched on exit.
    00186  */
    00187 ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
    00188
    00189
    00190 #ifdef __cplusplus
    00191 }
    00192 #endif
    00193
    00194 #endif